On his Twitter account, Rice said Ward's drunken-driving charge last week was "not a good look," The Baltimore Sun reported Monday.
Rice predicted Ward would be suspended for the season opener against the Ravens.
"People look up to you, Hines," Rice posted. "You've got a legacy in the NFL that no one can take away from you. But if you hurt somebody drunk driving, that takes away a lot."
"Drunk driving is one of those things that hits a soft spot in my life," Rice, who lost a cousin to a drunk driver in 1998, said. "I don't care if you're a Pittsburgh Steeler or a Baltimore Raven or whoever you are, if you get caught drunk driving, that's not a smart judgment.
"We make enough money," Rice said. "It's $150 for a car service for the rest of the night."
Ward was arrested July 9 after an officer in Georgia saw his Aston Martin weaving across lanes in the road and then hitting a curb, the Sun reported.
"I didn't put it on Twitter to disrespect," Rice said. "I just said 'it's not a good look.' When it comes across the ticker that you got arrested for a DUI, it's not a good look."